Lectures related to Theorem: Regularity Conditions and Rigorous Proofs

Proofs: Logic, Mathematics & Algorithms

Explores proof concepts, techniques, and applications in logic, mathematics, and algorithms.

Supremum Theorem

Explores the Supremum Theorem, its properties, proofs, and exercises.

Rigorous Proof of Differential Equations

Covers the rigorous proof of differential equations, emphasizing accuracy and precision.

Linear Independence: The Wronskian Concept

Explains the Wronskian and its role in determining linear independence of solutions to differential equations.

Newtonian Potential: Bounded Domains

Explores Newtonian potential in bounded domains, discussing its conditions and properties.

Fourier Inversion Formula

Covers the Fourier inversion formula, exploring its mathematical concepts and applications, emphasizing the importance of understanding the sign.

Inductive Propositions: Reasoning and Evaluation Techniques

Discusses inductive propositions, their definitions, and applications in reasoning and evaluation techniques in Coq.

Fundamental Solutions

Explores fundamental solutions in partial differential equations, highlighting their significance in mathematical applications.

Mathematical Induction: Principle and Example

Introduces the principle of mathematical induction through an example.

Differential Forms Integration

Covers the integration of differential forms on smooth manifolds, including the concepts of closed and exact forms.

Complex Integration and Cauchy's Theorem

Discusses complex integration and Cauchy's theorem, focusing on integrals along curves in the complex plane.

Calculus of Variations: Gradient Young Theorem

Covers the Gradient Young Theorem in the calculus of variations, discussing proofs and applications.

Recurrence: Induction

Covers the principle of induction for natural numbers and the importance of caution in its application.

Taylor Polynomials: Approximating Functions in Multiple Variables

Covers Taylor polynomials and their role in approximating functions in multiple variables.

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Inductive Propositions: Understanding Evaluation in Coq

Covers inductive propositions in Coq, focusing on evaluation rules for arithmetic expressions and their applications in defining partial and non-deterministic functions.

Modular Arithmetic: Foundations and Applications

Introduces modular arithmetic, its properties, and applications in cryptography and coding theory.

Linear Maps and the Duality Principle in Mathematics

Covers the duality principle in linear algebra and its implications in mathematics.

Proofs: Direct and Indirect Methods

Covers examples of direct and indirect proofs in mathematics.